Confirmation email doesn't delivered to name@example.com

I’m creating a buddypress social network for A/L student. When user tries to register using name@example.com email, He will not receive emails from buddypress. If user is entered such email as name@gmail.com there is no problem at all. I can’t identify what is going on. Please help me to proceed.

And you have tested a plain WP view of your site? i.e have you first tested that all aspects of primary functions work under your initial install of WP before moving on to activating BP and then testing it’s registration process – this is important to help you establish that your site works and if issues arise at what stage they did e.g. on activation of BP or of Welcome pack ( fyi Welcome Pack might not be quite current with latest BP)

You now need to narrow down the issue!

fwiw this sort of issue is nearly always one of a server configuration and/or of your MX records rather than an issue with either WP or BP both process and foreward emails quite happily without fail.